216 ON THE CONDUCTION OF HEAT IN CRYSTALS. isothermal surface passing through that point, that is, in a direction parallel to the radius vector drawn from the centre of the thermic sphere to the point of contact of a tangent plane drawn parallel to the isothermal surface at the point considered. Now the tangency of two surfaces is evidently unchanged by derivation. Hence, in a crystal, if we have given the direc- , tion of the isothermal surface at any point, we may find that of the flow of heat by the following construction. In a direction parallel to the isothermal surface at the given point draw a tangent plane to the thermic ellipsoid, and join the centre with ; the point of contact: the flow of heat will take place in a direc- i tion parallel to this joining line. In other words, the flow of | , heat will take place in a direction parallel to the diameter | which is conjugate to a plane parallel to the isothermal surface I ' at the given point. j;; I | \ \ 14. Conceive a plate bounded by parallel surfaces to be cut }V ' from a crystal, and heat to be applied towards its centre; and ;' suppose the lateral boundaries sufficiently distant to produce no !* ' j sensible influence on the result, so that we may regard the plate jr as infinite. In this case the auxiliary solid will likewise be an i infinite plate bounded by parallel surfaces. Now if heat be ; ! ; supplied according to any law at one point of such a plate, I • or at any number of points situated in the same normal, the | isothermal surfaces will be surfaces of revolution, having the 1 normal drawn through the source or sources of heat for their ; axis, and the isothermal curves in which the parallel faces are 1 , cut by the isothermal surfaces will be circles, having their centres in the points in which the faces are cut by the normal above-mentioned. Hence, in a crystalline plate, if heat be supplied according to any law at one point, or at any number of points situated in a line parallel to the diameter of the thermic ellipsoid which is conju- I gate to the planes of the faces, (a line which for brevity I will call the line of sources,) any particular isothermal surface will be a surface generated by an ellipse which has its plane parallel to ; the faces, its centre in the line of sources, and its principal axes parallel and proportional to those of the ellipse in which the thermic ellipsoid is cut by a plane parallel to the faces. In par-